Phase Diagram

Chapter 8Phase DiagramGraphical representations of what phases are present in a material system at various temperatures, pressures and composition.

ObjectivesDescribe cooling curves and phase diagrams and the type of information that may be extracted from them.Describe a binary isomorphous and binary eutectic phase diagram and be able to draw a generic diagram showing all phase regions and relevant information.Be able to apply tie line and lever rule to phase diagrams in order to determine the phase composition and phase fraction in a mixture.Cooling curveUsed to determine phase transition temperature for both pure metals and alloys.Obtained by recording the temperature of a materials vs time as it cools from a molten temperature until room temperature.Cooling CurvesA degree of undercooling is required for the formation of solid nuclei.

During region BCRegion BC also called plateau/ region of thermal arrestMetal is in the from of solid + liquid phaseTemperature remain constant because there is balance between heat lost by the metal through the mold and the latent heat supply by the solidifying metal

Cooling Curve for Pure Iron

May also provide information regarding the solid state phase transformation in metal6(1) Binary Isomorphous Alloy Systems A mixture of 2 metals is called binary alloyIn some binary metallic systems, the two elements are completely soluble in each other in both the liquid and solid states.In these systems, only a single type of crystal structure exists for all compositions of the components. Therefore they are called Isomorphous systemExample: Copper Nickel System. P+F = C+2

For pure water, at triple point, 3 phases coexist. There is one component (water) in the system. Therefore 3 + F = 1 + 2 F = 0. Degrees of freedom indicate number of variables (pressure, temperature and composition) that can be changed without changing number of phases. P = number of phases that coexist in a systemC = Number of componentsF = Degrees of freedomGibbs Phase RuleCopper-Nickel Phase Diagran

Thid diagram is for slow cooling or equilibrium condition.2. Liquidus represent a region of stability of liquid phase9The Lever RuleThe weight percentages of the phases in any two-phase region of a binary equilibrium phase diagram can be calculated by using the lever rule.

Example Problem 8.2A copper-nickel alloy contains 47 wt% Cu and 53 wt% Ni and is at 1300 C. Using the Cu-Ni phase diagram, answer the following:

What is the weight percent of copper in the liquid and solid phases at this temperature?What weight percent of this alloy is liquid and what weight percent is solid?(2) Binary Eutectic Alloy SystemsMany binary alloy systems have components that have limited solid solubility in each other.Terms related to Eutectic:Eutectic reaction: a phase transformation in which all the liquid phase transforms on cooling into two solid phases isothermally.Eutectic temperature: the temperature at which eutectic reaction takes place.Eutectic composition: the composition of the liquid phase that reacts to form two new solid phases at the eutectic temperature.Eutectic point: the point determined by the eutectic composition and temperature. Example, in lead (Pb) tin (Sn) system.

Example Problem 8.4Make phase analyses of the equilibrium (ideal) solidification of lead-tin alloys at the following points in the lead-tin phase diagram.At the eutectic composition just below 183C (eutectic temperature).The point c at 40% Sn and 230C.The point d at 40% Sn and 183C + T.The point e at 40% Sn and 183C T.Phase present:Compositions of phases:Amounts of phases:Example Problem 8.5One kilogram of an alloy of 70 percent Pb and 30 percent Sn is slowly cooled from 300C. Calculate the following:The weight percent of the liquid and proeutectic alpha at 250C.The weight percent of the liquid and proeutectic alpha just above the eutectic temperature (183C) and the weight in kilograms of these phases.The weight in kilograms of alpha and beta formed by the eutectic reaction.Example Problem 8.6A lead-tin (Pb-Sn) alloy contains 64 wt% proeutectic and 36 wt% eutectic + at 183 C T. Calculate the average composition of this alloy.